I also got some rely annoying start up problems with the TPS63700D.
I was follow the typical "Figure 15. Circuit for –12 Volt Output" from the datasheet page 13 application solution to make +/-12V supply for some Operation amplifiers
The thing is that +12V produced and start first to then supply +5V power and then the +5V supply the TPS63700D. So the supply to the TPS63700D start ~2.5ms after +12V and during that time I see that the -12V rail rise up to approximatly about +0.3V. Then the -12V ramp down to approx peek to 13.5V and direct after that the -12V rail turn off and fall back to +0.3V and will never turn on. If I manualy remove the +12V supply to all the Operation amplifier then there is no +0.3V on the -12V rail before startup and then the start up problem never occur. But this start up constraints is realy annoying because there is common to produce +/-12V supply to OP circuits (several OPA2277). Pleas answer if you have some solution for this. olle@dst.se